Parallel charge transfer reactions

Most real electrochemical reactions are not so simple. The truth is that most of them involve one or several adsoibed intermediates. A rather simple situation would involve two parallel (charge-transfer) reactions, such as... 

Due to the small amplitude of the superimposed voltage or current, the current-voltage relationship is linear and thus even charge-transfer reactions, which normally give rise to an exponential current-potential dependence (Chapter 4), appear as resistances, usually coupled with a capacitance. Thus any real ohmic resistance associated with the electrode will appear as a single point, while a charge transfer reaction (e.g. taking place at the tpb) will appear ideally as a semicircle, i.e. a combination of a resistor and capacitor connected in parallel (Fig. 5.29). 

The impedance data have been usually interpreted in terms of the Randles-type equivalent circuit, which consists of the parallel combination of the capacitance Zq of the ITIES and the faradaic impedances of the charge transfer reactions, with the solution resistance in series [15], cf. Fig. 6. While this is a convenient model in many cases, its limitations have to be always considered. First, it is necessary to justify the validity of the basic model assumption that the charging and faradaic currents are additive. Second, the conditions have to be analyzed, under which the measured impedance of the electrochemical cell can represent the impedance of the ITIES. 

Some experimental methods to compensate or to minimize the influence of the capacitive current have been reviewed by MacDonald [22]. The reader is directed to the same reference for the theoretical treatments of more complex systems involving parallel and consecutive charge transfer reactions, coupled chemical reactions, as well as of more sophisticated performances of large amplitude galvanostatic techniques, e.g. current reversal and cyclic methods. 

Faradic impedance (//) is directly related to the rates of charge transfer reactions at and near the electrode/electrode interface. As shown in Figure 3.1, the Faradaic impedance acts in parallel with the double-layer capacitance Cd, and this combination is in series with the electrolyte resistance Rei The parameters Rei and Cd in the equivalent circuit are similar to the idea of electrical elements. However, X/ is different from those normal electrical elements because Faradaic impedance is not purely resistive. It contains a capacitive contribution, and changes with frequency. Faradaic impedance includes both the finite rate of electron transfer and the transport rate of the electroactive reagent to the electrode surface. It is helpful to subdivide Zj into Rs and Cs, and then seek their frequency dependencies in order to obtain useful information on the electrochemical reaction. 

A schematic representation of the ideal electron-transfer rate and transfer coefficient as functions of potential for a semiconductor electrode is shown in Figure 18.2.6. Although there have been numerous studies with semiconductor electrodes, such ideal behavior is rarely seen (45, 47, 49, 57-59). Difficulties in such measurements include the presence of processes in parallel with the electron-transfer reaction involving dissolved reactant at the semiconductor surface, such as corrosion of the semiconductor material, effects of the resistance of the electrode material, and charge-transfer reactions that occur via surface states. 

In general, the impedance of solid electrodes exhibits a more complicated behavior than predicted by the Randles model. Several factors are responsible for this. Firstly, the simple Randles model does not take into account the time constants of adsorption phenomena and the individual reaction steps of the overall charge transfer reaction (Section 5.1). In fact the kinetic impedance may include several time constants, and sometimes one even observes inductive behavior. Secondly, surface roughness or non-uniformly distributed reaction sites lead to a dispersion of the capacitive time constants. As a consequence, in a Nyquist plot the semicircle corresponding to a charge-transfer resistance in parallel to the double-layer capacitance becomes flattened. To account for this effect it has become current practice in corrosion science and engineering to replace the double layer capacitance in the equivalent circuit by a... 

Electrochemistry at soft interfaces is a very interesting topic, as many different types of charge transfer reactions can take place in parallel and concomitantly. The different charge reactions include (i) ion transfer reactions where the flux of ions crossing the interface gives rise to a current (ii) assisted ion transfer reactions where the extraction of, for example, an aqueous ion by an organic soluble ionophore also gives rise to an ionic current and (iii)... 

The charge-transfer reaction closely parallels the thermal hydroalkylation of CP2MH2 (M = Mo and W) with related acceptors (fumarate and acrylate esters) [243], as well as the thermal reactions of R3MH (M = Sn, Si) with TCNE as the electron (proton) acceptor [244], e.g. ... 

The first kinetic relationships describing the inhibitory effect of halide ions at low anodic overvoltage followed by the sudden increase of current at the potential of unpolarizability were given by Heusler and Cartledge. The mechanism consists of two charge-transfer reactions occurring in parallel at the half-crystal position " " that is, at the kinks that are not covered by adsorbed anions, the main dissolution reaction occurs ... 

Whether due to matrix-analyte or analyte-analyte reactions, the analyte with the most favorable charge transfer thermodynamics will appear with greatest intensity in the mass spectrum. Since the thermodynamic picture of secondary plume reactions is not specific to any charge transfer reaction type, the same kind of suppression phenomena are expected for protonation, cationization, and electron transfer. As for the MSE, an increase in primary ions due to higher laser intensity reduces inter-analyte suppression since the matrix-analyte reactions are forced to the right. Also parallel to the MSE, ASE is favored by high analyte concentration. It is therefore normally preceded and accompanied by MSE. An example of both effects is shown in Figure 5.8. Because MSE and ASE are connected, suppression of one type of analyte ion by another can occur, and has been observed. ... 

In this section, we derive a general expression to describe activation polarization losses at a given electrode, known as the Butler-Volmer (BV) kinetic model. The BV model is not the only (or necessarily the most appropriate) model to describe a particular electrochemical reaction process. Nevertheless, it is a classical treatment of electrode kinetics that is widely applied to study and model a majority of the electrode kinetics of fuel cells. The BV model describes an electrochemical process limited by the charge transfer of electrons, which is appropriate for the ORR, and in most cases the HOR with pure hydrogen. The fundamental assumption of the BV kinetic model is that the reaction is rate hmited by a single electron transfer step, which may not actually be true. Some reactions may have two or more intermediate charge transfer reactions that compete in parallel or another intermediate step such as reactant adsorption (Tafel reaction from Chapter 2) may limit the overall reaction rate. Nevertheless, the BV model of an electrochemical reaction is standard fare for a student of electrochemistry and can be used to reasonably fit most fuel cell reaction behavior. 

COMMENTS The number of electrons transferred in the elementary charge transfer step at the cathode, c, can be a noninteger valne if derived experimentally since there can be more than one charge transfer reaction in parallel. The kinetic polarization voltages in this example are typical relative to one another. That is, the ORR losses usually dominate activation losses when pure hydrogen is nsed as the fnel. 

Where kjf, and kn, represent the adsorbtion and desorption reactions (which can be physical or chemical), respectively, and R represents the molar gas-phase concentration of the reacting species. The % reaction represents the fast-forward ion charge transfer reaction of the adsorbed species responsible for the current generation, and it is assumed the reverse reaction is negligible. It should be noted that other species or parallel reactions can also be included in the above formulation methodology. If 0 represents the fraction of the available catalysis sites that the adsorbed species occupies, we can then write... 

The impedance of a charge-transfer reaction at a porous electrode consisting of cylindrical pores is given in the previous section by Eq. (19.1) [23-26]. To simplify the calculations, the Faradaic impedance per unit real surface area was assumed to be potential-independent over a range of values that would exist along the entire pore, e. g., < 0.25 V, and thus consists only of a parallel combination of the charge transfer resistance and a double-layer capacitance, without a Warburg impedance. 

F r d ic Current. The double layer is a leaky capacitor because Faradaic current flows around it. This leaky nature can be represented by a voltage-dependent resistance placed in parallel and called the charge-transfer resistance. Basically, the electrochemical reaction at the electrode surface consists of four thermodynamically defined states, two each on either side of a transition state. These are (11) (/) oxidized species beyond the diffuse double layer and n electrons in the electrode and (2) oxidized species within the outer Helmholtz plane and n electrons in the electrode, on one side of the transition state and (J) reduced species within the outer Helmholtz plane and (4) reduced species beyond the diffuse double layer, on the other. 

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